Either one is correct. It depends on the context, as usual. Present Perfect Where have you been ?I've waited for ages! This is fine. The question is in the present perfect tense. It means that the person to whom you are speaking is here now.....that you are no longer waiting for the person. You stopped waiting before now...perhaps when you saw his/her car pull up in the parking lot, perhaps just before you started speaking. Since it still has a direct effect on the present moment you can use the present perfect tense. Present Perfect Continuous where have you been ?I've been waiting for ages. This is also fine. It means that you are still waiting for the person while you are speaking. Probably you have just seen the person this very moment and you feel like you are still waiting. You are letting the person know that you are waiting and have been waiting up to the present moment. There is a third possiblity that is acceptable in American English but not in British English. Simple past Where have you been? I waited for you for ages. In American usage this is equivalent to ... I have waited for you for ages. This is entirely in the past and implies that you stopped waiting for the person sometime in the past ....perhaps recently, perhaps a while ago.

I agree with Ms. Learner! In your inquiry "where have you been?" that is in present perfect continuous, must be followed with a statement (or answer) with the same tense. In a sense, they should be in 'parallel structure'. "have you been waiting for me? yes, I have been waiting for you." "did you wait for me? yes, I did" :)

Hello Honey If you don't understand this, may I suggest to take some sessions with an Italki teacher here ...

You should say 'Where have you been? I've been waiting for ages'. It's the present perfect continuous that you should use here (Not the present perfect simple). we use the continuous to say HOW LONG (for an activity that is still happening): 'She's still writing letters. She HAS BEEN WRITING letters all day.' 'How long HAVE you BEEN READING that book?' We use the simple to say HOW MUCH, HOW MANY or HOW MANY TIMES (for completed actions): 'She HAS WRITTEN ten letters today.' 'They'VE PLAYED tennis three times this week.' 'How much of that book HAVE you READ?'